# Capacity Optimality of OAMP in Coded Large Unitarily Invariant Systems

arXiv: https://arxiv.org/abs/2206.11680 · HTML: https://mlsanity.com/paper/2206.11680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 7 of 7)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Adaptive Neural Signal Detection for Massive MIMO](https://mlsanity.com/paper/1906.04610/) (2019)
- [Memory Approximate Message Passing](https://mlsanity.com/paper/2106.02237/) (2021)
- [Expectation Propagation for Approximate Inference: Free Probability Framework](https://mlsanity.com/paper/1801.05411/) (2018)
- [Deep Learning Based on Orthogonal Approximate Message Passing for CP-Free OFDM](https://mlsanity.com/paper/1905.02541/) (2019)
- [On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling](https://mlsanity.com/paper/2108.08503/) (2021)
- [Sufficient-Statistic Memory AMP](https://mlsanity.com/paper/2112.15327/) (2021)

## Abstract (arXiv)

This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrary fixed signal distribution, and forward error control (FEC) coding. Several area properties are established based on the state evolution of orthogonal approximate message passing (OAMP) in an un-coded LUIS. Under the assumptions that the state evolution for joint OAMP and FEC decoding is correct and the replica method is reliable, we analyze the achievable rate of OAMP. We prove that OAMP reaches the constrained capacity predicted by the replica method of the LUIS with an arbitrary signal distribution based on matched FEC coding. Meanwhile, we elaborate a constrained capacity-achieving coding principle for LUIS, based on which irregular low-density parity-check (LDPC) codes are optimized for binary signaling in the simulation results. We show that OAMP with the optimized codes has significant performance improvement over the un-optimized ones and the well-known Turbo linear MMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, constrained capacity-approaching bit error rate (BER) performances are observed under various channel conditions.